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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.util;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.ConvergenceException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /**<a name="line.23"></a>
<FONT color="green">024</FONT>     * Provides a generic means to evaluate continued fractions.  Subclasses simply<a name="line.24"></a>
<FONT color="green">025</FONT>     * provided the a and b coefficients to evaluate the continued fraction.<a name="line.25"></a>
<FONT color="green">026</FONT>     *<a name="line.26"></a>
<FONT color="green">027</FONT>     * &lt;p&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * References:<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;ul&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;li&gt;&lt;a href="http://mathworld.wolfram.com/ContinuedFraction.html"&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * Continued Fraction&lt;/a&gt;&lt;/li&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;/ul&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;/p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Id: ContinuedFraction.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.35"></a>
<FONT color="green">036</FONT>     */<a name="line.36"></a>
<FONT color="green">037</FONT>    public abstract class ContinuedFraction {<a name="line.37"></a>
<FONT color="green">038</FONT>        /** Maximum allowed numerical error. */<a name="line.38"></a>
<FONT color="green">039</FONT>        private static final double DEFAULT_EPSILON = 10e-9;<a name="line.39"></a>
<FONT color="green">040</FONT>    <a name="line.40"></a>
<FONT color="green">041</FONT>        /**<a name="line.41"></a>
<FONT color="green">042</FONT>         * Default constructor.<a name="line.42"></a>
<FONT color="green">043</FONT>         */<a name="line.43"></a>
<FONT color="green">044</FONT>        protected ContinuedFraction() {<a name="line.44"></a>
<FONT color="green">045</FONT>            super();<a name="line.45"></a>
<FONT color="green">046</FONT>        }<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * Access the n-th a coefficient of the continued fraction.  Since a can be<a name="line.49"></a>
<FONT color="green">050</FONT>         * a function of the evaluation point, x, that is passed in as well.<a name="line.50"></a>
<FONT color="green">051</FONT>         * @param n the coefficient index to retrieve.<a name="line.51"></a>
<FONT color="green">052</FONT>         * @param x the evaluation point.<a name="line.52"></a>
<FONT color="green">053</FONT>         * @return the n-th a coefficient.<a name="line.53"></a>
<FONT color="green">054</FONT>         */<a name="line.54"></a>
<FONT color="green">055</FONT>        protected abstract double getA(int n, double x);<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>        /**<a name="line.57"></a>
<FONT color="green">058</FONT>         * Access the n-th b coefficient of the continued fraction.  Since b can be<a name="line.58"></a>
<FONT color="green">059</FONT>         * a function of the evaluation point, x, that is passed in as well.<a name="line.59"></a>
<FONT color="green">060</FONT>         * @param n the coefficient index to retrieve.<a name="line.60"></a>
<FONT color="green">061</FONT>         * @param x the evaluation point.<a name="line.61"></a>
<FONT color="green">062</FONT>         * @return the n-th b coefficient.<a name="line.62"></a>
<FONT color="green">063</FONT>         */<a name="line.63"></a>
<FONT color="green">064</FONT>        protected abstract double getB(int n, double x);<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>        /**<a name="line.66"></a>
<FONT color="green">067</FONT>         * Evaluates the continued fraction at the value x.<a name="line.67"></a>
<FONT color="green">068</FONT>         * @param x the evaluation point.<a name="line.68"></a>
<FONT color="green">069</FONT>         * @return the value of the continued fraction evaluated at x.<a name="line.69"></a>
<FONT color="green">070</FONT>         * @throws ConvergenceException if the algorithm fails to converge.<a name="line.70"></a>
<FONT color="green">071</FONT>         */<a name="line.71"></a>
<FONT color="green">072</FONT>        public double evaluate(double x) throws ConvergenceException {<a name="line.72"></a>
<FONT color="green">073</FONT>            return evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE);<a name="line.73"></a>
<FONT color="green">074</FONT>        }<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>        /**<a name="line.76"></a>
<FONT color="green">077</FONT>         * Evaluates the continued fraction at the value x.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param x the evaluation point.<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param epsilon maximum error allowed.<a name="line.79"></a>
<FONT color="green">080</FONT>         * @return the value of the continued fraction evaluated at x.<a name="line.80"></a>
<FONT color="green">081</FONT>         * @throws ConvergenceException if the algorithm fails to converge.<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        public double evaluate(double x, double epsilon) throws ConvergenceException {<a name="line.83"></a>
<FONT color="green">084</FONT>            return evaluate(x, epsilon, Integer.MAX_VALUE);<a name="line.84"></a>
<FONT color="green">085</FONT>        }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /**<a name="line.87"></a>
<FONT color="green">088</FONT>         * Evaluates the continued fraction at the value x.<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param x the evaluation point.<a name="line.89"></a>
<FONT color="green">090</FONT>         * @param maxIterations maximum number of convergents<a name="line.90"></a>
<FONT color="green">091</FONT>         * @return the value of the continued fraction evaluated at x.<a name="line.91"></a>
<FONT color="green">092</FONT>         * @throws ConvergenceException if the algorithm fails to converge.<a name="line.92"></a>
<FONT color="green">093</FONT>         * @throws MaxCountExceededException if maximal number of iterations is reached<a name="line.93"></a>
<FONT color="green">094</FONT>         */<a name="line.94"></a>
<FONT color="green">095</FONT>        public double evaluate(double x, int maxIterations)<a name="line.95"></a>
<FONT color="green">096</FONT>            throws ConvergenceException, MaxCountExceededException {<a name="line.96"></a>
<FONT color="green">097</FONT>            return evaluate(x, DEFAULT_EPSILON, maxIterations);<a name="line.97"></a>
<FONT color="green">098</FONT>        }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>        /**<a name="line.100"></a>
<FONT color="green">101</FONT>         * Evaluates the continued fraction at the value x.<a name="line.101"></a>
<FONT color="green">102</FONT>         * &lt;p&gt;<a name="line.102"></a>
<FONT color="green">103</FONT>         * The implementation of this method is based on the modified Lentz algorithm as described<a name="line.103"></a>
<FONT color="green">104</FONT>         * on page 18 ff. in:<a name="line.104"></a>
<FONT color="green">105</FONT>         * &lt;ul&gt;<a name="line.105"></a>
<FONT color="green">106</FONT>         *   &lt;li&gt;<a name="line.106"></a>
<FONT color="green">107</FONT>         *   I. J. Thompson,  A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."<a name="line.107"></a>
<FONT color="green">108</FONT>         *   &lt;a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf"&gt;<a name="line.108"></a>
<FONT color="green">109</FONT>         *   http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf&lt;/a&gt;<a name="line.109"></a>
<FONT color="green">110</FONT>         *   &lt;/li&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         * &lt;/ul&gt;<a name="line.111"></a>
<FONT color="green">112</FONT>         * &lt;b&gt;Note:&lt;/b&gt; the implementation uses the terms a&lt;sub&gt;i&lt;/sub&gt; and b&lt;sub&gt;i&lt;/sub&gt; as defined in<a name="line.112"></a>
<FONT color="green">113</FONT>         * &lt;a href="http://mathworld.wolfram.com/ContinuedFraction.html"&gt;Continued Fraction @ MathWorld&lt;/a&gt;.<a name="line.113"></a>
<FONT color="green">114</FONT>         * &lt;/p&gt;<a name="line.114"></a>
<FONT color="green">115</FONT>         *<a name="line.115"></a>
<FONT color="green">116</FONT>         * @param x the evaluation point.<a name="line.116"></a>
<FONT color="green">117</FONT>         * @param epsilon maximum error allowed.<a name="line.117"></a>
<FONT color="green">118</FONT>         * @param maxIterations maximum number of convergents<a name="line.118"></a>
<FONT color="green">119</FONT>         * @return the value of the continued fraction evaluated at x.<a name="line.119"></a>
<FONT color="green">120</FONT>         * @throws ConvergenceException if the algorithm fails to converge.<a name="line.120"></a>
<FONT color="green">121</FONT>         * @throws MaxCountExceededException if maximal number of iterations is reached<a name="line.121"></a>
<FONT color="green">122</FONT>         */<a name="line.122"></a>
<FONT color="green">123</FONT>        public double evaluate(double x, double epsilon, int maxIterations)<a name="line.123"></a>
<FONT color="green">124</FONT>            throws ConvergenceException, MaxCountExceededException {<a name="line.124"></a>
<FONT color="green">125</FONT>            final double small = 1e-50;<a name="line.125"></a>
<FONT color="green">126</FONT>            double hPrev = getA(0, x);<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>            // use the value of small as epsilon criteria for zero checks<a name="line.128"></a>
<FONT color="green">129</FONT>            if (Precision.equals(hPrev, 0.0, small)) {<a name="line.129"></a>
<FONT color="green">130</FONT>                hPrev = small;<a name="line.130"></a>
<FONT color="green">131</FONT>            }<a name="line.131"></a>
<FONT color="green">132</FONT>    <a name="line.132"></a>
<FONT color="green">133</FONT>            int n = 1;<a name="line.133"></a>
<FONT color="green">134</FONT>            double dPrev = 0.0;<a name="line.134"></a>
<FONT color="green">135</FONT>            double cPrev = hPrev;<a name="line.135"></a>
<FONT color="green">136</FONT>            double hN = hPrev;<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>            while (n &lt; maxIterations) {<a name="line.138"></a>
<FONT color="green">139</FONT>                final double a = getA(n, x);<a name="line.139"></a>
<FONT color="green">140</FONT>                final double b = getB(n, x);<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>                double dN = a + b * dPrev;<a name="line.142"></a>
<FONT color="green">143</FONT>                if (Precision.equals(dN, 0.0, small)) {<a name="line.143"></a>
<FONT color="green">144</FONT>                    dN = small;<a name="line.144"></a>
<FONT color="green">145</FONT>                }<a name="line.145"></a>
<FONT color="green">146</FONT>                double cN = a + b / cPrev;<a name="line.146"></a>
<FONT color="green">147</FONT>                if (Precision.equals(cN, 0.0, small)) {<a name="line.147"></a>
<FONT color="green">148</FONT>                    cN = small;<a name="line.148"></a>
<FONT color="green">149</FONT>                }<a name="line.149"></a>
<FONT color="green">150</FONT>    <a name="line.150"></a>
<FONT color="green">151</FONT>                dN = 1 / dN;<a name="line.151"></a>
<FONT color="green">152</FONT>                final double deltaN = cN * dN;<a name="line.152"></a>
<FONT color="green">153</FONT>                hN = hPrev * deltaN;<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>                if (Double.isInfinite(hN)) {<a name="line.155"></a>
<FONT color="green">156</FONT>                    throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,<a name="line.156"></a>
<FONT color="green">157</FONT>                                                   x);<a name="line.157"></a>
<FONT color="green">158</FONT>                }<a name="line.158"></a>
<FONT color="green">159</FONT>                if (Double.isNaN(hN)) {<a name="line.159"></a>
<FONT color="green">160</FONT>                    throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,<a name="line.160"></a>
<FONT color="green">161</FONT>                                                   x);<a name="line.161"></a>
<FONT color="green">162</FONT>                }<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>                if (FastMath.abs(deltaN - 1.0) &lt; epsilon) {<a name="line.164"></a>
<FONT color="green">165</FONT>                    break;<a name="line.165"></a>
<FONT color="green">166</FONT>                }<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>                dPrev = dN;<a name="line.168"></a>
<FONT color="green">169</FONT>                cPrev = cN;<a name="line.169"></a>
<FONT color="green">170</FONT>                hPrev = hN;<a name="line.170"></a>
<FONT color="green">171</FONT>                n++;<a name="line.171"></a>
<FONT color="green">172</FONT>            }<a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>            if (n &gt;= maxIterations) {<a name="line.174"></a>
<FONT color="green">175</FONT>                throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,<a name="line.175"></a>
<FONT color="green">176</FONT>                                                    maxIterations, x);<a name="line.176"></a>
<FONT color="green">177</FONT>            }<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>            return hN;<a name="line.179"></a>
<FONT color="green">180</FONT>        }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>    }<a name="line.182"></a>




























































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